Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

First of all, what is the mathematical relationship between measured linewidth (usually in units of magnetic field) and spin relaxation time? I see papers talk about spin relaxation times in terms of linewidths but I have no idea how to correlate the size of the linewidth to an actual time.

Second, is the measured linewidth in NMR or ESR experiments related to $T_2^{\ast}$ only. If you want just $T_2$, you would have to do spin-echo, right? If that is the case, how is $T_1$ determined?

share|cite|improve this question
Is linewidth the image-resolution? – kame Feb 26 '11 at 22:05
Very naively speaking, linewidth ~ $\Delta E \propto 1/\Delta T$, where $\Delta T$ is the spin relaxation time. – user346 Feb 27 '11 at 3:18

The theory is rather generic Fourier transform: if you have a perfectly non-decaying oscillation $e^{i\omega_0 t}$ (with real $k$) then the transform gives a perfectly sharp spectrum as a delta function $\delta(\omega - \omega_0)$. But if the excitation decays $e^{i\omega_0 t} e^{-k t}$ then we get $\delta(\omega - \omega_0 - i k)$, which has a real part that is broadened: $1/\left({(\omega-\omega_0)^2 + k^2}\right)$.

Now, usually this manifests as some sort of sweep time, as experimentally you would drive the system at some changing frequency $\omega$ and observe the driven amplitude.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.